How To Keep Humidity from Ruining Fold-Top Desk?

Q: We inherited a gorgeous mid-century teak hutch/desk with a fold-up leaf that locks closed. The desk spent all of its post-Denmark days in California, and we live in Austin. When we moved it in, the leaf opened and closed freely, but since we've set it up, the wood has expanded, ostensibly because of humidity from some recent rain we've had, and now it won't close.

We're not talking just-barely-won't-close. It's off by about 3 mm! I'm worried that Austin is just more humid than So Cal and it's just going to be stuck open for the rest of its life — which is not how we planned to use it. Any ideas? Do I need a dehumidifier just for my desk? Is there risk of the desk cracking if we don't do something now?